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Transactions of the American Mathematical Society

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Hereditarily normal manifolds of dimension greater than one may all be metrizable


Authors: Alan Dow and Franklin D. Tall
Journal: Trans. Amer. Math. Soc. 372 (2019), 6805-6851
MSC (2010): Primary 54A35, 54D15, 54D45, 54E35, 03E05, 03E35, 03E65; Secondary 54D20, 03E55
DOI: https://doi.org/10.1090/tran/7916
Published electronically: August 28, 2019
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Abstract: P. J. Nyikos has asked whether it is consistent that every hereditarily normal manifold of dimension greater than one is metrizable, and he proved that it is if one assumes the consistency of a supercompact cardinal, and, in addition, that the manifolds are hereditarily collectionwise Hausdorff. We are able to omit these extra assumptions.


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Additional Information

Alan Dow
Affiliation: Department of Mathematics and Statistics, University of North Carolina, Charlotte, North Carolina 28223
Email: adow@uncc.edu

Franklin D. Tall
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
Email: f.tall@math.utoronto.ca

DOI: https://doi.org/10.1090/tran/7916
Keywords: Hereditarily normal, manifold, metrizable, coherent Souslin tree, proper forcing, $\mr{PFA}(S)[S]$, locally compact, $P$-ideal, perfect preimage of $\w_1$, sequentially compact.
Received by editor(s): September 23, 2015
Received by editor(s) in revised form: August 2, 2016, February 20, 2017, and November 28, 2017
Published electronically: August 28, 2019
Additional Notes: The first author’s research was supported by NSF grant DMS-1501506
The second author’s research was supported by NSERC grant A-7354
Article copyright: © Copyright 2019 American Mathematical Society